- We present a simple model for the bidirectional dynamics of actin bundles with alternating polarities in gliding assays with nonprocessive myosin motors. The bundle is represented as an elastic chain consisting of monomers with positive and negative polarities. The motion of the bundle is induced by the pulling forces of the underlying motors which stochastically attach to the monomers and, depending on their polarities, pull them in the right or left direction. We demonstrate that perfectly apolar chains consisting of equal numbers of monomers with positive and negative polarities may exhibit biased bidirectional motion with a nonzero drift. This effect is attributed to the elastic tension developed in the chain due to the action of the myosin motors. We also show that as a result of this tension, the attachment probability of the motors is greatly reduced and becomes strongly dependent on the length of the chain.